Quiz%202

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Quiz 2

• Average 26
• Distribution
• Min 2, Max 50
• 00-10 6
• 11-20 30
• 21-30 33
• 31-40 25
• 51-50 12
• It you need to see your point status please see
  me after class or in my office.

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Test Review Problem 1

• 5 points The ratio of the maximum acceleration
  to the maximum velocity (amax/vmax) for an object
  in simple harmonic motion is
• a) k b) w c) d) 1/w
• Answer

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Test Review Problem 2

• 5 points A mass of 10.0kg is at rest on a
  horizontal surface, the coefficient of static
  friction between the mass and surface is 0.330.
  What horizontal force must be applied to move the
  mass?
• a) 32.3N b)98.0N c)1N d)297N
• Answer

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Test Review Problem 3

• 5 points A wheel of radius 0.15m is rotating
  at an angular velocity of 2.2 rads/sec. What is
  the velocity of the edge of the wheel?
• a) 1m/s b)0.068m/s c)14.7m/s d)0.33m/s
• Answer

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Test Review Problem 4

• 5 points On a planet with a radius 1.5 times
  greater than that of earth but with the same
  mass, what would be the acceleration of gravity
  at the surface?
• a) 4.36 m/s2 b) 0.23 m/s2 c) 6.53 m/s2 d)
  0.15 m/s2
• Answer

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Test Review Problem 5

• 5 points Suppose planet A and planet B are each
  orbited by satellites at the same radii r.
  However the velocity of the satellite orbiting
  planet A is four times that of the velocity of
  the satellite orbiting planet B. What is mA/mB ,
  the ratio of the mass of planet A to planet B?

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Test Review Problem 6

• 10 points A space laboratory is rotating to
  create artificial gravity, a person standing in a
  room with the floor at a radius of 2150m feels
  entirely at home since the centripetal
  acceleration is equal to g. What is the velocity
  of the person and angular velocity of the
  laboratory?

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Test Review Problem 7
y
FN
x
v05m/s
(5pnts)
m
Ffr

• 15 points A sled is traveling at 5.00 m/s along
  a horizontal stretch of snow. The coefficient of
  kinetic friction is mk0.0500. Draw the freebody
  diagram for the sled. What is the sleds
  acceleration and how far does it travel in the
  horizontal direction before stopping?

mg
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Unit 4 Conservation of Energy

• Definition of Work (7-1, 7-2, 7-3)
• Examples of Work, Definition of Energy and the
  link to Work (7-3, 7-4, 7-5)
• Potential Energy (8-1, 8-2)
• Problem Solving with the Conservation of Energy
  (8-3, 8-4)
• Applications of Conservation of Energy (8-5,
  8-6, 8-7, 8-8, 8-9).

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Generalized Potential Energy

• For gravity the potential energy is
• And the work is given by a line integral
• This can be generalized for any conservative force

• But this does not hold for non-conservative
  forces such as friction because the integral
  would depend on the path and not the endpoints.

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Elastic Potential Energy

• When uncompressed or stretched the end of the
  spring at the right rests at x0.
• When decompressed the spring can increase the
  velocity of the ball and in other words, do work
  on the ball.
• According to Hookes Law, if a person is to
  compress the spring he or she must press with a
  force FPkx.
• According to the 3rd Law the spring pushes back
  with FS-kx.

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Elastic Potential Energy
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Comments on Potential Energy

• Potential energy stored by a system has the
  potential to do work at a later time
• Gravity A brick held aloft - Umgh
• Elastic A compressed and locked spring- U
  (1/2)kx2
• A potential energy is always associated with a
  conservative force.
• The choice U0 is arbitrary, examples
• Gravity surface of the earth
• Elastic relaxed position
• An object does not possess potential energy but a
  system does
• Gravity mass and the earth
• Elastic mass and the spring.
• Electrical the positive and negative charges.

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Conservation of Mechanical Energy

• Lets just consider a conservative system (earth
  and object, spring and mass)
• One in which the work does not depend on the path
  taken
• Or equivalently one for which the work around a
  closed path is zero
• One in which energy can be transformed from
  kinetic energy to potential and back again.
• By the work-energy principle we know that

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Whats it Mean?

• We have defined a conserved quantity, the total
  mechanical energy which is a constant. In
  symbols KUconstant .
• Thus there can be well described transformation
  of energy from kinetic energy to potential
  energy. If K decreases then U must increase by
  an equivalent amount.
• If only one object has kinetic energy then
  E(1/2)mv2Uconstant. And for two positions
  (1/2)mv12U1(1/2)mv22U2
• Here its clear why it doesnt matter where we
  set the potential energy to zero. It would appear
  on both sides of the equation and cancel.

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The Classic Example The Falling Rock

• Anywhere along the path the total mechanical
  energy is E (1/2)mv2mgh.
• When dropped, the rock has no velocity so K
  (1/2)mv20 but it has potential energy Umgh
• As it falls, K increases and the potential energy
  decreases so that the total energy is constant.
• At the surface, K is at a maximum and the
  potential at a minimum, Umgh0.

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Whats it good for?

• If h3.0m, calculate the speed when the rock is
  1.0 m above the ground.

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• Imagine the roller coaster starts at rest from
  the hill top at 40.0m.
• What is
• The speed at the bottom of the hill?
• The height at half this speed?
• Lets put y0, U0 at the bottom of the hill.

Note this would have been very hard to solve
with Fma since the vertical and horizontal
motion are coupled and curved. Energy
conservation avoided all that!
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What about Elastic Potential Energy?
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A Toy Dart Gun

• A dart of mass 0.100kg is pressed against the
  spring of a toy gun. The spring (k250N/m) is
  compressed 6.0cm and released.
• What is the darts speed when leaves the spring
  at the relaxed position x0?

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• In the horizontal direction the only force (and
  potential energy) is due to the spring.
• In the vertical direction gravity and the normal
  force cancel one another.
• However after it leaves the barrel we are also
  equipped to describe the trajectory!
• We can use the new equation with point 1 as
  corresponding to the compressed spring and point
  2 the moment of departure.

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What about a Vertical Spring?

• Then we have kinetic energy and two types of
  potential energy gravitational and elastic.
• The equation can be extended to
• And we can have energy transforming from kinetic
  energy to two forms of potential energy and back
  again

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A Bungee Jumper.

• A 75-kg student bungee jumps off a bridge. The
  cord has a spring constant of 50N/m starts to
  stretch at 15m.
• How far will the student fall before coming to a
  stop? Ignore air-friction.

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Conclusions

• Mechanical Energy and Conservation of Energy are
  very powerful concepts.
• Friday well discuss non-ideal situations,
  gravitational potential energy at all distances,
  power, and stabel and unstable equilibrium.

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